1. Field of the Invention
The present invention relates to a differential amplifier circuit comprised of bipolar transistors or Metal-Oxide-Semiconductor Field-Effect Transistors (MOSFETs) and more particularly, to a differential amplifier circuit having an improved transconductance linearity within a wide input voltage range, and a multiplier using the differential amplifier circuit, which are formed on a bipolar or MOS semiconductor integrated circuit device (IC) and is operable at a supply voltage as low as approximately 1.9 V.
2. Description of the Prior Art
A differential amplifier circuit having a superior transconductance linearity within a comparatively wide input voltage range has been known as an "Operational Transconductance Amplifier (OTA)".
A first conventional bipolar OTA is shown in FIG. 1, which is termed "Gilbert gain cell". This OTA was disclosed in IEEE Journal of Solid-State Circuits, Vol. SC-3, No. 4, pp. 353-365, December, 1968, entitled "A Precise Four-Quadrant Analog Multiplier with Subnanosecond Response", and written by B. Gilbert.
As shown in FIG. 1, the "Gilbert gain cell" includes first and second balanced differential pairs. The first differential pair is composed of npn bipolar transistors Q101 and Q102. The second differential pair is composed of npn bipolar transistors Q105 and Q106.
In the first differential pair, an emitter of the transistor Q101 is connected to one end of a constant current sink sinking a constant current I.sub.0. An emitter of the transistor Q102 is connected to one end of another constant current sink sinking the same constant current I.sub.0 as that of the sink for the transistor Q101. The other ends of the two current sinks are connected to the ground. The transistors Q101 and Q102 are driven by the corresponding current sinks, respectively.
The emitters of the transistors Q101 and Q102 are connected to each other through an emitter resistor R101 having a resistance R.
Bases of the transistors Q101 and Q102 are connected to a pair of input terminals, respectively. A differential input voltage V.sub.i as an input signal of the first conventional OTA of FIG. 1 is applied across the bases of the transistors Q101 and Q102 through the pair of input terminals.
Two diode-connected npn bipolar transistors Q103 and Q104 are provided as loads of the corresponding transistors Q101 and Q102, respectively. Specifically, collectors of the transistors Q101 and Q102 are connected to emitters of the transistors Q103 and Q104, respectively. A base and a collector of the transistor Q103 are coupled together to be applied with a power supply voltage V.sub.CC. A base and a collector of the transistor Q104 are coupled together to be connected to be applied with the same power supply voltage V.sub.CC.
In the second differential pair composed of the transistors Q105 and Q106, emitters of the transistors Q105 and Q106 are coupled together to be connected to one end of a common constant current sink sinking a constant current I.sub.1. The other end of the current sink is grounded. No emitter resistor is provided for the transistors Q105 and Q106.
Bases of the transistors Q105 and Q106 are connected to the collectors of the transistors Q102 and Q101, respectively.
A differential output current .DELTA.I.sub.C as an amplified output signal of the conventional OTA (i.e., the Gilbert gain cell) is defined as the difference between collector currents I.sub.C.sup.+ and I.sub.C.sup.- of the transistors Q105 and Q106. Therefore, the output current .DELTA.I.sub.C is expressed as .DELTA.I.sub.C =I.sub.C.sup.+ -I.sub.C.sup.-. The output current .DELTA.I.sub.C is differentially derived from the collectors of the transistors Q105 and Q106.
In the first differential pair, the difference between collector currents of the transistors Q101 and Q102 is converted to the voltages through the diode-connected load transistors Q103 and Q104. Through this current-to-voltage conversion, the difference of the collector currents of the transistors Q101 and Q102 is logarithmically compressed.
The converted voltages thus obtained are derived from the emitters of the load transistors Q103 and Q104, and then applied across the bases of the transistors Q105 and Q106 in the second differential pair. The second differential pair differentially amplifies the applied voltages and output the differential output current .DELTA.I.sub.C at the collectors of the transistors Q105 and Q106.
Next, the operation of the conventional Gilbert gain cell of FIG. 1 is explained in detail below.
Here, supposing that the base-width modulation (i.e., the Early voltage) is ignored, a collector current I.sub.C of a bipolar transistor is typically expressed as the following equation (1) ##EQU1##
In the equation (1), V.sub.BE is the base-to-emitter voltage of the transistor, and I.sub.S is the saturation current thereof. V.sub.T is the thermal voltage defined as V.sub.T =kT/q, where k is the Boltzmann's constant, T is absolute temperature in degrees Kelvin, and q is the charge of an electron.
In the following analysis, for the sake of simplification, it is supposed that the common-base current gain factor of the transistor is approximately equal to unity and therefore, the base current can be ignored.
When the differential input voltage V.sub.i is applied across the bases of the transistors Q101 and Q102 in the first differential pair, the following equation (2) is established around the loop consisting of the input voltage and the two base-emitter junctions because of the Kirchhoff's voltage law. EQU V.sub.IN =V.sub.BE1 -V.sub.BE2 +Ri (2)
In the equation (2), V.sub.BE1 and V.sub.BE2 are the base-to-emitter voltages of the transistors Q101 and Q102, and i is a current flowing through the emitter resistor R101.
Supposing that R i&gt;&gt;V.sub.BE1 -V.sub.BE2 is established, the current i is expressed as the following equation (3). ##EQU2##
The current i flowing through the emitter resistor R101 further flows through the diode-connected transistors Q103 and Q104 as a differential current, resulting in a differential output voltage V.sub.0 between the emitters of the transistors Q103 and Q104 (or, collectors of the transistors Q101 and Q102).
The differential output voltage V.sub.0 of the first differential pair is expressed by the following equation (3a) as ##EQU3##
It is seen from the equation (3a) that the output voltage V.sub.0 is in a logarithmically compressed form of the current i. This means that the voltage V.sub.0 is logarithically proportional to the current i.
The differential output voltage V.sub.0 is then applied across the bases of the transistors Q105 and Q106 to be amplified, resulting in the differential output current .DELTA.I.sub.C as an amplified output signal of V.sub.0.
Typically, in a balanced differential pair of two bipolar transistors having no emitter resistor, a differential output current is approximately, exponentially proportional to a differential input voltage. Accordingly, the differential output current .DELTA.I.sub.C is in an exponentially expanded form of the differential output voltage V.sub.0.
Thus, the output current .DELTA.I.sub.C is proportional to the current i flowing through the emitter resistor R101. This means that the current i can be derived from the collectors of the transistors Q105 and Q106 (i.e., the output terminals).
With the conventional Gilbert gain cell shown in FIG. 1, however, a problem that a complete linear behavior cannot be realized occurs, because it contains the approximation as shown in the above equation (3). Satisfactory linearity in the OTA behavior can be realized only when the value of the resistance R of the emitter resistor R101 and the values of the constant currents I.sub.0 and I.sub.1 are suitably designed.
The conventional Gilbert gain cell of FIG. 1 has another problem that the signal-to-noise ratio (S/N) is remarkably degraded. This is because the input signal V.sub.i is logarithmically compressed and then, exponentially expanded.
A second conventional bipolar OTA is shown in FIG. 2, which is termed the "Caprio's quad", and realizes the approximately, completely linear behavior. This OTA was disclosed in IEE Electronics Letters, 22nd Mar. 1973, Vol. 9, No. 6, pp. 147-148, entitled "Precision Differential Voltage-Current Converter", and written by R. Caprio.
As shown in FIG. 2, four npn bipolar transistors Tr1, Tr2, Tr3, and Tr4 are connected in cascode. Specifically, an input voltage V is applied across bases of the transistor Tr1 and Tr3 with the polarity shown in FIG. 2. Output currents I.sub.C1 and I.sub.C3 of the OTA of FIG. 2 are derived from collectors of the transistors Tr1 and Tr3.
An emitter of the transistor Tr1 is connected to a base of the transistor Tr4 and a collector of the transistor Tr2. An emitter of the transistor Tr3 is connected to a base of the transistor Tr2 and a collector of the transistor Tr4.
An emitter of the transistor Tr2 is connected to one end of a constant current sink sinking a constant current (I.sub.0 /2). An emitter of the transistor Tr4 is connected to one end of another constant current sink sinking the same constant current (I.sub.0 /2). An emitter resistor with a resistance R.sub.E is connected to the emitters of the transistors Tr2 and Tr4.
The operation of the conventional OTA termed the "Caprio's quad" in FIG. 2 is as follows;
Since the transistors Tr1 and Tr2 are cascode-connected and the transistors Tr3 and Tr4 are also cascode-connected, the following equations (4) and (5) are established. EQU V.sub.BE1 =V.sub.BE2 (4) EQU V.sub.BE3 =V.sub.BE4 (5)
In the equations (4) and (5), V.sub.BE1, V.sub.BE2, V.sub.BE3, and V.sub.BE4 are the base-to-emitter voltages of the transistors Tr1, Tr2, Tr3, and Tr4, respectively.
Here, the positive and negative voltage shifts of the input voltage V, which are generated by the transistors Tr1, Tr2, Tr3, and Tr4, are defined as V.sub.S.sup.+ and V.sub.S.sup.-, respectively. Since the bases and collectors of the transistors Tr2 and Tr4 are cross-coupled, the positive and negative voltage shifts V.sub.S.sup.+ and V.sub.S.sup.- are equal to each other, and expressed as the following equation (6). EQU V.sub.S.sup.+ =V.sub.BE3 +V.sub.BE2 =V.sub.BE1 +V.sub.BE4 =V.sub.S.sup.-(6)
Therefore, the voltages V.sub.S.sup.+ and V.sub.S.sup.- applied to the emitter resistor is equal in magnitude and opposite in polarity to the input voltage V.
Accordingly, the following equation (7) is established. EQU V=R.sub.E i (7)
The output currents I.sub.C1 and I.sub.C3 are given by the following equations (8) and (9), respectively. ##EQU4##
From the equations (8) and (9), the differential output current .DELTA.I, which is defined as .DELTA.I=(I.sub.C1 -I.sub.C3), is (-2V/R.sub.E). Thus, the differential output current .DELTA.I is opposite in polarity to the input voltage V.
The conventional OTA termed the "Caprio's quad" in FIG. 2 has a problem that the differential output current .DELTA.I is opposite in polarity to the input voltage V.
Another problem of the "Caprio's quad" is that the maximum value of the input voltage V is as low as approximately .+-.400 mV. This is because the transistors Tr2 and Tr4 will saturate if the input voltage V is large.
A further problem of the "Caprio's quad" is that the power supply voltage is not decreased, because the transistors Tr1, Tr2, Tr3, and Tr4 are cascode-connected in two stages.
A third conventional bipolar OTA is shown in FIG. 3, which is termed the "Gilbert-cell transconductor". This OTA was disclosed in IEEE Journal of Solid-State Circuits, Vol. 28, No. 12, pp. 1246-1253, December, 1993, entitled "A 2.5-V Active Low-Pass Filter Using All n-p-n Gilbert Cells with a 1-V.sub.P-P Linear Input Range", and written by M. Koyama et al.
In FIG. 3, a first balanced differential pair of npn-bipolar transistors Q201 and Q202 serves as a voltage-to-current (V-I) converter. A second balanced differential pair of npn-bipolar transistors Q203 and Q204 serves as an arc hyperbolic tangent function (tanh.sup.-1) circuit. A third balanced differential pair of npn-bipolar transistors Q205 and Q206 serves as a hyperbolic tangent function (tanh) circuit.
A differential input voltage V.sub.id is applied across bases of the transistors Q201 and Q202. An emitter resistor R201 with a resistance R.sub.EE is connected to emitters of the transistors Q201 and Q202. A current i flows through the resistor R201. The emitter of the transistor Q201 is connected to a collector of the transistor Q203. The emitter of the transistor Q202 is connected to a collector of the transistor Q204.
A collector of the transistor Q201 is applied with a power supply voltage V.sub.CC through a constant current source supplying a constant current (I.sub.1 /2). A collector of the transistor Q202 is applied with the power supply voltage V.sub.CC through another constant current source supplying the same constant current (I.sub.1 /2).
The collector of the transistor Q201 is further connected to a base of the transistor Q203 through a constant voltage source supplying a constant voltage V.sub.LS. Similarly, the collector of the transistor Q202 is further connected to a base of the transistor Q204 through another constant voltage source supplying the same constant voltage V.sub.LS. The two voltage sources serve to shift the voltage level at the bases of the transistors Q203 and Q204.
Emitters of the transistors Q203 and Q204 are coupled together to be connected to the ground through an emitter resistor R202.
In the third differential pair, bases of the transistors Q205 and Q206 are connected to the bases of the transistors Q204 and Q203 of the second transistor pair, respectively. The bases of the transistors Q205 and Q206 are applied with the voltage difference between the base voltages of the transistors Q203 and Q204, i.e., .DELTA.V.sub.i. The voltage .DELTA.V.sub.i is proportional to the arc hyperbolic tangent of the current i, i.e., (tanh.sup.-1 i).
Emitters of the transistors Q205 and Q206 are coupled together to be connected to the ground through a constant current sink sinking a constant current I.sub.2. Collectors of the transistors Q205 and Q206 are applied with the power supply voltage V.sub.CC through corresponding constant current sources supplying the same constant current (I.sub.2 /2).
Output currents I.sub.01 and I.sub.02 are differentially derived from the collectors of the transistors Q205 and Q206, respectively. The differential output current .DELTA.I.sub.0 is proportional to the hyperbolic tangent of the input voltage .DELTA.V.sub.1, i.e., (tanh .DELTA.V.sub.i).
With the third conventional OTA termed the "Gilbert-cell transconductor" in FIG. 3, the transistors Q201 and Q202 of the first differential pair are driven by the constant currents with the same current value (I.sub.1 /2), respectively. Therefore, the base-to-emitter voltages V.sub.BE1 and V.sub.BE2 of the transistors Q201 and Q202 are equal. Thus, EQU V.sub.BE1 =V.sub.BE2 (10)
is established.
The voltage applied to the emitter resistor R201 of the transistors Q201 and Q202 is equal to the input voltage V.sub.id. That is, EQU V.sub.id =iR.sub.EE (11)
is established.
Therefore, the output currents I.sub.C3 and I.sub.C4 of the second differential pair of the transistors Q203 and Q204 are expressed as the following equations (12) and (13), respectively. ##EQU5##
It is seen from the equations (12) and (13) that the current I.sub.C3 decreases as the input voltage V.sub.id increases, and that the current I.sub.C4 increases as the input voltage V.sub.id increases.
The second differential pair of the transistors Q203 and Q204 serves as the arc hyperbolic tangent function (tanh.sup.-1) circuit. If the differential output current .DELTA.I.sub.0 is defined as the difference between the currents I.sub.C3 and I.sub.C4, i.e., .DELTA.I.sub.0 =I.sub.C3 -I.sub.C4, the differential voltage .DELTA.V.sub.i is expressed as .DELTA.V.sub.1 =tanh.sup.-1 (.DELTA.I.sub.0).
Further, the third balanced differential pair of the transistors Q205 and Q206 serves as the hyperbolic tangent function (tanh) circuit. Accordingly, .DELTA.I.sub.0 =tanh(.DELTA.V.sub.i) is established.
As a result, the arc hyperbolic tangent function of the second differential pair of the transistors Q203 and Q204 cancels the hyperbolic tangent function of the third differential pair of the transistors Q205 and Q206. Thus, the linear operation is obtained.
The relationship or polarity of the currents I.sub.C3 and I.sub.C4 with the input voltage V.sub.id is adjusted by replacing the connections of the transistors Q203 and Q204 to the transistors Q205 and Q206.
The conventional OTA of FIG. 3 termed the "Gilbert Gain Cell" has a problem that large degradation in S/N occurs because of the logarithmically compression with the use of the function (tanh.sup.-1) and exponentially expansion with the use of the function (tanh).
Another problem of the conventional OTA of FIG. 3 is that the power supply voltage cannot be reduced due to the existence of the (tanh.sup.-1) and (tanh) function circuits.
To improve the conventional Gilbert gain cell to thereby realize the complete linearity in the OTA behavior,
a fourth conventional bipolar OTA is shown in FIG. 4, which was developed to improve the conventional Gilbert gain cell of FIG. 1. This OTA was disclosed in Proceedings of the 1994 IEICE fall conference, No. A-12, entitled "Low-Voltage Operable Bipolar OTA", written by M. Hirota et al.
The fourth conventional bipolar OTA of FIG. 4 seems to be able to realize the complete linearity in the OTA behavior.
As shown in FIG. 4, a first differential pair is composed of npn bipolar transistors Q301 and Q302. An emitter of the transistor Q301 is connected to one end of a constant current sink sinking a constant current I.sub.1. An emitter of the transistor Q302 is connected to one end of another constant current sink sinking the same constant current I.sub.1 as that of the sink for the transistor Q301. The other ends of the two current sinks are connected to the ground. The transistors Q301 and Q302 are driven by the corresponding current sinks, respectively.
The emitters of the transistors Q301 and Q302 are connected to each other through an emitter resistor R301 having a resistance R.
Bases of the transistors Q301 and Q302 are connected to a pair of input terminals T201 and T202, respectively.
An input voltage (V.sub.IN /2) is applied to the base of the transistor Q301. Another input voltage (-V.sub.IN /2) is applied to the base of the transistor Q302.
Two constant current sources supplying the same constant current 2I.sub.0 are provided for loads of the respective transistors Q301 and Q302. Collectors of the transistor Q301 and Q302 are connected to ends of the corresponding current sources, respectively.
A second differential pair is composed of npn bipolar transistors Q303 and Q304. Emitters of the transistors Q303 and Q304 are connected to each other through an emitter resistor R302 having the same resistance R as that of the resistor R301. Collectors of the transistors Q303 and Q304 are applied with a power supply voltage V.sub.CC through corresponding current sources supplying the same constant current 2I.sub.1, respectively. Bases of the transistors Q303 and Q304 are commonly connected to a positive end of a constant voltage source supplying a dc constant voltage V.sub.bias.
A third differential pair is composed of npn bipolar transistors Q305 and Q306. Emitters of the transistors Q305 and Q306 are directly coupled together to be connected to the ground through a resistor R303. Collectors of the transistors Q305 and Q306 are connected to the emitters of the transistors Q303 and Q304, respectively.
An npn transistor Q307 and a constant current source supplying a constant current I.sub.3 are provided for the transistor Q305. An emitter of the transistor Q307 is connected to the ground through this current source. A collector of the transistor Q307 is applied with the power supply voltage V.sub.CC. A base of the transistor Q307 is connected to the collector of the transistor Q303.
Similarly, an npn transistor Q308 and a constant current source supplying the same constant current I.sub.3 as that of the current source for the transistor Q307 are provided for the transistor Q306. An emitter of the transistor Q308 is connected to the ground through this current source. A collector of the transistor Q308 is applied with the power supply voltage V.sub.CC. A base of the transistor Q308 is connected to the collector of the transistor Q304.
The transistors Q307 and its corresponding constant current sink sinking the current I.sub.3 have a function of level-shifting the current flowing through the transistor Q305. The transistors Q308 and its corresponding constant current sink sinking the current I.sub.3 have a function of level-shifting the current flowing through the transistor Q306.
The two constant current sources supplying the same constant current 2I.sub.1, which serve as the loads of the respective transistors Q301 and Q302, commonly serve as loads of the respective transistors Q303 and Q304.
A fourth differential pair is composed of npn bipolar transistors Q309 and Q310. Emitters of the transistors Q309 and Q310 are coupled together to be connected to the ground through a constant current sink sinking a constant current 2I.sub.2. Collectors of the transistors Q309 and Q310 are applied with the supply voltage V.sub.CC through corresponding current sources supplying the same constant current I.sub.2, respectively.
Output currents I.sub.OUT1 and I.sub.OUT2 are differentially derived from the collectors of the transistors Q309 and Q310, respectively, resulting in a differential output current .DELTA.I.sub.OUT as an amplified output signal of the conventional OTA of FIG. 4, which is defined as .DELTA.I.sub.OUT =I.sub.OUT1 -I.sub.OUT2.
The first differential pair including the resistor R301 constitutes an input circuit. The second and third differential pairs including the resistor R302 constitute a non-linearity compensation circuit for compensating the non-linearity of the differential input voltage V.sub.IN. The fourth differential pair constitutes an output circuit.
Next, the operation of the conventional OTA of FIG. 4 is explained below.
When the differential input voltage V.sub.IN is applied across the bases of the transistors Q301 and Q302 of the first differential pair, the following equation (14) is established around the loop consisting of the input voltage and the two base-emitter junctions because of the Kirchhoff's voltage law EQU V.sub.IN =V.sub.BE1 -V.sub.BE2 +Ri.sub.R (14)
where V.sub.BE1 and V.sub.BE2 are the base-to-emitter voltages of the transistors Q301 and Q302, and i.sub.R is a current flowing through the emitter resistor R301.
From the equation (14), the current i.sub.R is expressed by the following equation as ##EQU6##
In this conventional OTA shown in FIG. 4, the two current sources supplying the same current 2I.sub.1 are commonly used as the loads for the first differential pair of the transistors Q301 and Q302 and the second differential pair of the transistors Q303 and Q304. Therefore, the collector currents of the transistors Q301 and Q303 are equal and as a result, the base-to-emitter voltages V.sub.BE1 and V.sub.BE3 are equal.
Similarly, the collector currents of the transistors Q302 and Q304 are equal and as a result, the base-to-emitter voltages V.sub.BE2 and V.sub.BE4 are equal.
Since the emitter resistor R302 for the transistors Q303 and Q304 has the same resistance value R as that of the resistor R301, a current i.sub.R ' flowing through the resistor R302 can be expressed as the following equation (16). ##EQU7##
Accordingly, currents I.sub.5 and I.sub.6 flowing through the transistors Q305 and Q306 can be obtained as the following equations (17) and (18), respectively. ##EQU8##
It is seen from the equations (17) and (18) that an output voltage V.sub.0 between the bases of the transistors Q305 and Q306 is proportional to a differential current defined as (I.sub.5 -I.sub.6)=(2V.sub.IN /R).
The output voltage is inputted into the fourth differential pair of the transistors Q307 and Q308 and therefore, a differential output current .DELTA.I.sub.OUT (=I.sub.OUT1 -I.sub.OUT2), which is derived from the collectors of the transistors Q307 and Q308 and is proportional to (2V.sub.IN /R), can be obtained.
Since the current i.sub.R ' flowing through the emitter resistor R302 shown by the equation (16) is supplied from the transistors Q303 and Q304, the equation (16) is established only under the condition that both of the currents flowing through the transistors Q303 and Q304 are greater than the value of [(V.sub.BE4 -V.sub.BE3)/R].
This means that conventional bipolar OTA of FIG. 4 does not realize a completely linear OTA behavior.
Also, this OTA has the same problem as in the Gilbert gain cell that the signal-to-noise ratio (S/N) is remarkably degraded.
FIG. 5 shows the well-known Gilbert multiplier cell.
In FIG. 5, npn bipolar transistors Q401 and Q402 form a first emitter-coupled differential pair, npn bipolar transistors Q403 and Q404 form a second emitter-coupled differential pair, and npn bipolar transistors Q405 and Q406 form a third emitter-coupled differential pair.
Collectors of the transistors Q401, Q402, Q403 and Q404 are cross-coupled. A collector of the transistor Q405 is connected to the coupled emitters of the transistors Q401 and Q402. A collector of the transistor Q406 is connected to the coupled emitters of the transistors Q403 and Q404. The coupled emitters of the transistors Q405 and Q406 are connected to a constant current sink sinking a constant current I.sub.0. Bases of the transistors Q401 and Q404 are coupled together. Bases of the transistors Q402 and Q403 are also coupled together.
A first input voltage V.sub.x is applied across the coupled bases of the transistors Q401 and Q404 and those of the transistors Q402 and Q403. A second input voltage V.sub.y is applied across the bases of the transistors Q405 and Q406.
The third differential pair of the transistors Q405 and Q406 and the corresponding constant current sink constitute a differential voltage-current converter.
A collector current of the transistor Q405 is expressed as [(I.sub.0 /2)+(I.sub.y /2)], and a collector current of the transistor Q406 is expressed as [(I.sub.0 /2)-(I.sub.y /2)], where I.sub.y is a collector current generated by the input voltage V.sub.y.
An output current I.sup.+ is derived from the coupled collectors of the transistors Q401 and Q403, and another output current I.sup.- is derived from the coupled collectors of the transistors Q402 and Q404. A differential output current .DELTA.I of the Gilbert multiplier cell containing the multiplication result is obtained by the difference of the two output currents, i.e., .DELTA.I=I.sup.+ -I.sup.-.
When the Gilbert multiplier cell of FIG. 4 is used as a mixer circuit, an input signal is applied to the coupled bases of the transistors Q401 and Q404 and those of the transistors Q402 and Q403, and at the same time, a local signal is applied across the bases of the transistors Q405 and Q406. In this case, the non-linearity of the input signal tends to cause the third-order distortion in mixer characteristics.
Therefore, the linearity of the voltage-current converter, which is formed by the transistors Q405 and Q406 driven by the constant current sink, needs to be improved.
Additionally, in the Gilbert multiplier cell in FIG. 5, the differential output current .DELTA.I is expressed as EQU .DELTA.I=I.sup.+ -I.sup.- =I.sub.0 [tanh(V.sub.x /2V.sub.T).cndot.tanh(V.sub.y /2V.sub.T)].
When V.sub.x .ltoreq.V.sub.T and V.sub.y .ltoreq.V.sub.T, the differential output current .DELTA.I is approximated as EQU .DELTA.I.apprxeq.I.sub.0 [(V.sub.x /2V.sub.T).cndot.(V.sub.y /2V.sub.T)].
An OTA is an essential, basic function block in analog signal applications. Recently, fabrication processes for large-scale integrated circuit devices (LSIs) have been becoming finer and finer and as a result, the supply voltage for the LSIs has been decreasing from 5 V to 3 V, or lower. This tendency has been increasing the necessity for the low-voltage circuit technique more and more.
Also, the above-described conventional OTAs of FIGS. 1 to 4 are capable of low-voltage operation at approximately 3 or 2 V when the input voltage range providing the linear operation is 1 V peak-to-peak (i.e., 1 V.sub.P-P). However, they have the various problem described previously.